One of the approaches to manipulate MnBi${}_2$Te${}_4$ properties is the magnetic dilution, which inevitably affects the interplay of magnetism and band topology in the system. In this work, we carried out angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory (DFT) calculations for analysing changes in the electronic structure of Mn${}_{1-x}$Ge${}_x$Bi${}_2$Te${}_4$ that occur under parameter x variation. We consider two ways of Mn/Ge substitution: (i) bulk doping of the whole system; (ii) surface doping of the first septuple layer. For the case (i), the experimental results reveal a decrease in the value of the bulk band gap, which should be reversed by an increase when the Ge concentration reaches a certain value. Ab-initio calculations show that at Ge concentrations above 50%, there is an absence of the bulk band inversion of the Te $p_z$ and Bi $p_z$ contributions at the $\Gamma$-point with significant spatial redistribution of the states at the band gap edges into the bulk, suggesting topological phase transition in the system. For case (ii) of the vertical heterostructure Mn${}_{1-x}$Ge${}_x$Bi${}_2$Te${}_4$/MnBi${}_2$Te${}_4$, it was shown that an increase of Ge concentration in the first septuple layer leads to effective modulation of the Dirac gap in the absence of significant topological surface states of spatial redistribution. The results obtained indicate that surface doping compares favorably compared to bulk doping as a method for the Dirac gap value modulation.

Experimental investigations of antiferromagnetic topological insulator MnBi₂Te₄ have shown that the energy gap in samples may vary in a wide range. Since the energy gap is a key parameter of this system when used in developing new functional electronic devices, the reason for variation of the MnBi₂Te₄ energy gap at the Dirac point and its possible interrelation with magnetic interactions are matters of great importance and call for thorough analysis. To elucidate factors influencing the energy gap, we analyzed the variation of the electronic structure of the given topological insulator with surface van der Waals gap. Calculation data have shown that the energy gap at such structure modifications may vary in a wide range from 80–88 meV to 4–5 meV because of an intense spatial redistribution of topological surface states between septuple-layer MnBi₂Te₄ blocks with oppositely directed Mn magnetic moments. Our results suggest that the spatial localization of topological surface states is a primary factor governing the value of the energy gap, this localization being strongly dependent on structure modifications on the crystal surface.

The possibility of changing the bandgap value of topological surface states in materials based on the MnBi₂Te₄ intrinsic antiferromagnetic topological insulator is investigated using ab initio calculations. These materials are produced by the substitution of nonmagnetic chemical elements (A = Si, Ge, Sn, Pb) for magnetic metal atoms (Mn) in the surface (Mn_{1 – x}A_xBi₂Te₄/MnBi₂Te₄) septuple layer. The results exhibit a s-ignificant modulation of the bandgap in a wide range from 60 meV to 0 meV with an increase in the doping level x. Moreover, it is found that the bandgap behavior depends on a dopant. Namely, a monotonic dependence of the bandgap on x is found for Si and Ge, whereas the bandgap minimum at x = 0.75 exists for Sn and Pb. The results obtained in this work suggest that the main mechanism of the bandgap modulation in the materials under study is a change in the localization of topological surface states.

В данной работе с помощью ab initio расчетов была исследована возможность изменения энергетической запрещенной зоны в топологических поверхностных состояниях систем на основе собственного антиферромагнитного топологического изолятора MnBi2Te4. Системы получены путем замещения атомов магнитного металла (Mn) на атомы немагнитных элементов (A=Si, Ge, Sn, Pb) в поверхностном семислойном блоке (Mn1−xAxBi2Te4/MnBi2Te4). Результаты исследования показали значительную модуляцию величины энергетической запрещенной зоны в широком диапазоне от 60 мэВ до 0мэВ при увеличении концентрации замещения x. Более того, было обнаружено, что выбор замещающего элемента влияет на характер изменения величины энергетической запрещенной зоны. Так, для Si и Ge была выявлена монотонная зависимость величины энергетической запрещенной зоны от x, в то время как для Sn и Pb минимальное значение энергетической запрещенной зоны наблюдалось при x = 0.75. Полученные в работе результаты позволяют предположить, что основным механизмом модуляции энергетической запрещенной зоны в исследованных системах является изменение локализации топологических поверхностных состояний.